which we refer to as the penalized maximum log-likelihood function.
This estimator is applied to match a sigmoid-function to a set of measurements \(x_1,...,x_m\)  and corresponding Bernoulli-variables \(y_1,...,y_n \in \lbrace -1,1\rbrace ^m\) , where additionally sparsity is promoted in the parameters \(w_i\) .
Replacing \(\left\Vert \cdot \right\Vert _0\)  by \(\left\Vert \cdot \right\Vert _1\)  in (REF ), we obtain a convex composite optimization problem, which can be tackled by FISTA or proximal BFGS methods, compare [1]}.
